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In this paper, a generalized modified mesh current method is developed for the simulation of lightning-caused electromagnetic transients on thin-wire structures above and buried in lossy ground. Four coupling mechanisms among conductors, namely, inductive coupling, resistive coupling, conductive coupling, and capacitive coupling, are all considered. In comparison to the method based the electric-field integral equation and the method of moments, the new formulation has several attractive features: 1) it is accurate from dc to MHz and it does not have the low-frequency breakdown problem when part of the thin-wire structure is exposed in the air; 2) it has a time-domain form and can be easily implemented in a circuit-simulator with external components connected; and 3) it is much faster because the inverse of the system matrix only needs to be evaluated once. The method is developed based on ElectroMagnetoqQuasiStatic assumption, therefore it is suitable for thin-wire structures with relatively small spatial scales. As an application, the method is used to simulate the lightning transients on a building with a lightning protection system and a simple TN-C-S power supply system. The protection effectiveness of the surge protective devices is evaluated.